abstract. let mn;m be the set of n-by-m matrices with entries inthe field of real numbers. a matrix r in mn = mn;n is a generalizedrow substochastic matrix (g-row substochastic, for short) if re e, where e = (1; 1; : : : ; 1)t. for x; y 2 mn;m, x is said to besgut-majorized by y (denoted by x sgut y ) if there exists ann-by-n upper triangular g-row substochastic matrix r such thatx = ry . th...

The m-th root of the diagonal of the upper triangular matrix Rm in the QR decomposition of AXB = QmRm converges and the limit is given by the moduli of the eigenvalues of X with some ordering, where A,B,X ∈ Cn×n are nonsingular. The asymptotic behavior of the strictly upper triangular part of Rm is discussed. Some computational experiments are discussed.

in this paper, we introduce the concept of the   generalized aip-rings as a generalization of the generalized quasi-   baer rings   and generalized p.p.-rings. we show that the class of the generalized aip-rings is closed under direct products and morita invariance. we also characterize the 2-by-2 formal upper triangular matrix rings of this new class of rings. finally, we provide sever...

In this paper we define multiplication between intuitionistic fuzzy matrices (IFMs) and we derive the conditions for a block IFM to be regular. Also a method to find the generalized inverse of it with the help of the generalized inverses of the blocks of the original matrix is described. Again, it is shown that a block intuitionistic fuzzy matrix can be decomposed into an upper triangular idemp...

In this paper, we investigate GPU based parallel triangular solvers systematically. The parallel triangular solvers are fundamental to incomplete LU factorization family preconditioners and algebraic multigrid solvers. We develop a new matrix format suitable for GPU devices. Parallel lower triangular solvers and upper triangular solvers are developed for this new data structure. With these solv...

An efficient method for the computation to high relative accuracy of the LDU decomposition of an n × n row diagonally dominant M–matrix is presented, assuming that the off–diagonal entries and row sums are given. This method costs an additional O(n) elementary operations over the cost of Gaussian elimination, and leads to a lower triangular, column diagonally dominant matrix and an upper triang...

Abstract In this paper, we study the images of multilinear graded polynomials on algebra upper triangular matrices $UT_n$ . For positive integers $q\leq n$ , classify these $UT_{n}$ endowed with a particular elementary ${\mathbb {Z}}_{q}$ -grading. As consequence, obtain natural {Z}}_{n}$ We apply classification in order to give new condition for polynomial terms identities so that traceless it...

The main purpose of this paper is to give an improvement numerical radius inequality for upper triangular operator matrix.